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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 945 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.x + 7y = 45 and 7x + y = −21 →
  2. 2.3x − 5y = −3 and 6x + 3y = 72 →
  3. 3.x + 6y = 4 and 6x + y = −11 →
  4. 4.3x + y = −29 and x + 3y = −31 →
  5. 5.9x + 5y = 112 and 5x + 9y = 112 →
  6. 6.6x + 3y = −57 and 6x + 2y = −48 →
  7. 7.3x + 4y = −14 and 4x + 3y = −7 →
  8. 8.6x + 6y = 24 and 4x + 5y = 17 →
  9. 9.3x + 2y = 37 and 6x + 3y = 66 →
  10. 10.6x + 3y = 6 and 3x + 6y = 39 →
  11. 11.2x − 4y = −8 and x − 5y = −22 →
  12. 12.6x − 3y = −12 and 4x + 2y = 0 →
  13. 13.4x + 2y = −30 and 2x + 4y = −12 →
  14. 14.3x + 6y = −39 and 4x − y = −16 →
  15. 15.5x + 3y = −50 and 3x + 5y = −46 →
  16. 16.5x + 6y = −48 and 6x + 5y = −51 →
  17. 17.2x + 3y = −1 and 3x + 2y = 6 →
  18. 18.x − 5y = −25 and 5x + 6y = −1 →
  19. 19.6x + 5y = −55 and 6x − 2y = −20 →
  20. 20.6x + 8y = 44 and 8x + 6y = 40 →
  21. 21.4x + 3y = −11 and 3x + 4y = 4 →
  22. 22.8x + 6y = 54 and 6x + 8y = 58 →
  23. 23.2x + 8y = −60 and 8x + 2y = 0 →
  24. 24.3x − 2y = −24 and x + 4y = 6 →
  25. 25.3x + 7y = 8 and 7x + 3y = 32 →
  26. 26.2x + 8y = −22 and 8x + 2y = 2 →
  27. 27.x − 2y = −8 and 5x + y = 48 →
  28. 28.6x + 2y = 12 and 2x + 6y = −12 →
  29. 29.2x − 4y = 26 and 5x − 6y = 49 →
  30. 30.3x − 5y = −12 and x − y = −6 →
  31. 31.2x + 8y = 76 and 8x + 2y = 64 →
  32. 32.3x + 4y = 30 and 4x + 3y = 33 →
  33. 33.2x + 3y = −11 and 4x + y = 13 →
  34. 34.7x + y = 42 and x + 7y = 54 →
  35. 35.2x + 2y = −2 and 5x + 2y = 13 →
  36. 36.6x − 3y = 9 and 6x + 2y = 54 →
  37. 37.6x + 7y = 21 and 7x + 6y = 31 →
  38. 38.5x + 5y = 20 and 4x − 4y = 24 →
  39. 39.6x + 3y = 3 and 4x − 6y = −38 →
  40. 40.4x + 2y = 36 and 2x + 4y = 24 →

Answer key

  1. x = −4, y = 7
  2. x = 9, y = 6
  3. x = −2, y = 1
  4. x = −7, y = −8
  5. x = 8, y = 8
  6. x = −5, y = −9
  7. x = 2, y = −5
  8. x = 3, y = 1
  9. x = 7, y = 8
  10. x = −3, y = 8
  11. x = 8, y = 6
  12. x = −1, y = 2
  13. x = −8, y = 1
  14. x = −5, y = −4
  15. x = −7, y = −5
  16. x = −6, y = −3
  17. x = 4, y = −3
  18. x = −5, y = 4
  19. x = −5, y = −5
  20. x = 2, y = 4
  21. x = −8, y = 7
  22. x = 3, y = 5
  23. x = 2, y = −8
  24. x = −6, y = 3
  25. x = 5, y = −1
  26. x = 1, y = −3
  27. x = 8, y = 8
  28. x = 3, y = −3
  29. x = 5, y = −4
  30. x = −9, y = −3
  31. x = 6, y = 8
  32. x = 6, y = 3
  33. x = 5, y = −7
  34. x = 5, y = 7
  35. x = 5, y = −6
  36. x = 6, y = 9
  37. x = 7, y = −3
  38. x = 5, y = −1
  39. x = −2, y = 5
  40. x = 8, y = 2

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